Context. Cow survival is an important trait for dairy farm profitability and animal welfare, yet it is difficult to improve because of its complexity arising, in part, from varied reasons for culling and delay in getting actual culling data, which leads to low accuracy and instability of genetic predictions. Aims. To explore the benefits of partitioning the cow survival trait into 'early survival' (survival coded as a binary trait from the first to the second lactation) and 'late survival' (survival from the second to later lactations) on genetic predictions in addition to predictors of culling decisions. Methods. The raw phenotypic survival records for 1 619 542 Holstein and 331 996 Jersey cows were used in our study. All cows within each herd were allocated to either a reference or validation set. The accuracy and stability of genetic predictions were compared across lactations in the validation set. Further, we estimated the phenotypic and genetic correlation between overall, early or late cow survival and production, type, workability, and fertility traits using bivariate sire models. Key results. The heritability of overall survival in Jerseys (0.069 ± 0.003) was higher than in Holsteins (0.044 ± 0.001). The heritability of early survival was higher than that of late survival in Holstein (0.039 ± 0.002 vs 0.036 ± 0.001) and Jersey (0.080 ± 0.006 vs 0.053 ± 0.003). The genetic correlation between early and late survival was high in both breeds (0.770 ± 0.017 in Holstein and 0.772 ± 0.028 in Jersey). Adding survival information up to the sixth lactation had a large effect on genetic predictions of overall and late survival, whereas the predictions of early survival remained the same across lactations. Milk and protein yields, somatic cell score, fertility and temperament were highly correlated with early survival in Holstein and Jersey. However, the genetic correlations between production, type or workability traits and late survival were generally weaker than those and early survival. Conclusions. Early and late survival should be considered as different traits in genetic evaluations, because they are associated with different culling decisions. Implications. Partitioning cow survival into early and late survival and analysing them as two correlated traits could improve the accuracy and the stability of estimated breeding values compared with analysing overall survival as a single trait.